الشفاء بتعریف حقوقِ مصطفیٰ ﷺ کا تعارفی و تجزیاتی مطالعہ An Analytical Study of the “Al-Shifā Ba Ta‘rīf-e-Ḥuqūq-e-Muṣṭafā”

The most prominent and living name among the African biographers is Qazi Ayaz Mālkī. His book “Al-Shifā Ba Ta‘rīf-e-Ḥuqūq-e-Muṣṭafā” has an important place in the books of Sīrah and also has the status of the most popular book among all kinds of people. This book is also called Kitab-e-Shifā (meaning the one who revives hearts and heals from heart diseases). The reason for writing this book was that the people were becoming oblivious to the obligatory status and virtues of the Holy Prophet ﷺ and were becoming completely incapable of paying their dues. In these circumstances, the demand for preparation and compilation of a collection of rights and manāqibs related to it became intense and he compiled this magnificent book. On the one hand, it teaches love and respect for the Prophet (peace and blessings of Allah be upon him) and on the other hand, it mentions his rights and rewards for fulfilling them. The writing style of the book is simple and smooth as well as eloquent. The book is not so long that it would be too long for the reader to comprehend, nor is it so short that it would not be possible to get access to the concepts and demands due to its brevity. The people have made this book their favorite and have been studying it and the biographers have adopted Al-Shifā as an authoritative and reliable source. Because of its importance and usefulness, an introductory and analytical study of this book will be presented in this article.

Neutrino Oscillation Parameters and Optimization Techniques

We present a global analysis, through traditional and a new technique, of the solar neutrino data using total event rates of chlorine (Homestake), Gallax+GNO, SAGE, Superkamiokande and SNO detectors for the two neutrino case. The traditional is the grid search technique, where we calculate well known chi-square (χ 2 ) function for neutrino oscillations for a grid of the parameters ∆m2 and tan2 θ. We find our global minima in the LMA region with ∆m2 = 2.512 · 10−5 eV2 and tan2 θ = 0.3981. We also find local minimum χ 2 values in different regions of the parameter space. The new technique we chose is Differential Evolution. The Differential Evolution is a population based stochastic algorithm for optimization of real valued non-linear non-differentiable objective functions that has become very popular during the last decade. We combined this with the traditional grid based method for optimization of solar neutrino oscillation parameters ∆m2 and tan2 θ. We explore regions around the minima found in the global analysis using Differential Evolution for the fine tuning of the parameters, allowing even those values of the parameters which do not lie on any grid. We note as much as 4 times decrease in χ 2 value in the SMA region and even better goodness-of-fit as compared to our grid-based results. All this indicates a way out of the impasse faced due to CPU limitations of the larger grid method.